Can you please help me with this logic problem?

Pi should have read the problem a little more carefully, because the construction sites are only 500 miles apart. If each team drives 300 miles away from the office, then that puts them 600 miles apart when they arrive at their respective destinations, which is definitely a no-no by the terms of the problem. Notice too that the problem doesn't state or imply that the two sites are equidistant from the office. It merely states that the office is between the two sites. So we cannot equate the two distances the teams traveled.

Use the distance equation d = rt for team A, and d' = r't' for team B. Then d is the distance team A drives from the engineering office, and d' is the distance team B drives from the office. Also, d + d' = 500 mi. We are given that team A's rate is 50 mph, so r = 50. We are also given that team A leaves 1 hour earlier than team B. So letting t' be team B's time, then team A's time is t = 1 + t'. We are also given that team B's speed is 60 mph. So r' = 60. Putting all this mess together, we can extract these equations:

For team A:

d = rt

d = 50 (1 + t')

For team B:

d' = r't'

d' = 60t'.

Since d + d' = 500 mi, we add the two equations above to get this:

d + d' = rt + r't'

500 = 50 (1 + t') + 60t'

500 = 50 + 50t' + 60t'

500 - 50 = 110t'

450 = 110t'

450/110 = t'

45/11 = t'

1 + 45/11 = 11/11 + 45/11 = 56/11 = t.

Now we need to verify that the distances add up:

Team A: d = (50 mph)(56/11 hr) = (2800/11) mi ≈ 254.5454...mi.

Team B: d' = (60 mph)(45/11 hr) = (2700/11) mi ≈ 245.4545...mi.

d + d' ≈ 254.5454...mi + 245.4545...mi ≈ 499.9999...mi.

Notice that we can easily round the last number above to 500 mi.

So team A traveled approximately 254.55 miles, and team B traveled approximately 245.45 miles to their respective sites.

Hi,

If team B traveled at 60 mph for x hours, then team A traveled at 50 mph at 50 mph.

If they arrived simultaneously, then 50(x + 1) = 60x

5x + 50 = 60x

50 = 10x

x = 5

60(5) = 300, so each team traveled 300 miles to their site. <==ANSWER

I hope that helps!! :-)